Recursive Magic State Distillation on the Surface Code

TL;DR

This paper presents a recursive method to reduce the resource cost of preparing magic states in surface code quantum computing using lattice surgery, improving efficiency for large code distances.

Contribution

It introduces a recursive 15-to-1 magic state distillation protocol that lowers the resource overhead in surface code implementations.

Findings

Reduces the number of qubits and cycles needed for magic state preparation.

Provides a recursive implementation that scales with code distance.

Highlights the need for a lower physical error threshold for effective magic state distillation.

Abstract

I reduce the cost to prepare magic states with lattice surgery operations on the surface code by using a recursive implementation of 15-to-1 magic state distillation. On a rotated surface code with distance $d$, $|T\rangle$ preparation requires a $d$-by-$3 d$ grid of data qubits for up to $15 d$ error correction cycles, and $|CCZ\rangle$ preparation requires a $3 d$-by-$2 d$ grid for up to $10.5 d$ cycles. However, a significantly lower physical error threshold than that of the underlying surface code is required to match the error probability of the output magic state with the logical error rate of the output surface code at large code distances.